On calibrated and separating sub-actions
| hal.structure.identifier | Instituto de Matemática, Estatística e Computação Científica [Brésil] [IMECC] | |
| dc.contributor.author | GARIBALDI, Eduardo | |
| hal.structure.identifier | Instituto de Matémàtica | |
| dc.contributor.author | LOPES, Artur | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | THIEULLEN, Philippe | |
| dc.date.accessioned | 2024-04-04T02:37:50Z | |
| dc.date.available | 2024-04-04T02:37:50Z | |
| dc.date.created | 2009-04-24 | |
| dc.date.issued | 2010 | |
| dc.identifier.issn | 1678-7544 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190835 | |
| dc.description.abstractEn | We consider a one-sided transitive subshift of finite type $ \sigma: \Sigma \to \Sigma $ and a Hölder observable $ A $. In the ergodic optimization model, one is interested in properties of $A$-minimizing probability measures. If $\bar A$ denotes the minimizing ergodic value of $A$, a sub-action $u$ for $A$ is by definition a continuous function such that $A\geq u\circ \sigma-u + \bar A$. We call contact locus of $u$ with respect to $A$ the subset of $\Sigma$ where $A=u\circ\sigma-u + \bar A$. A calibrated sub-action $u$ gives the possibility to construct, for any point $x\in\Sigma$, backward orbits in the contact locus of $u$. In the opposite direction, a separating sub-action gives the smallest contact locus of $A$, that we call $\Omega(A)$, the set of non-wandering points with respect to $A$. We prove that, under certain conditions on $\Omega(A)$, any calibrated sub-action is of the form $u(x)=u(x_i)+h_A(x_i,x)$ for some $x_i\in\Omega(A)$, where $h_A(x,y)$ denotes the Peierls barrier of $A$. We also prove that separating sub-actions are generic among Hölder sub-actions. We present the proofs in the holonomic optimization model, a formalism which allows to take into account a two-sided transitive subshift of finite type $(\hat \Sigma, \hat \sigma)$. | |
| dc.description.sponsorship | Hamilton-Jacobi et théorie KAM faible : à l'interface des EDP, systèmes dynamiques lagrangiens et symboliques - ANR-07-BLAN-0361 | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.title.en | On calibrated and separating sub-actions | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| bordeaux.journal | Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society | |
| bordeaux.page | 587 - 612 | |
| bordeaux.volume | 40 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00387289 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00387289v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Boletim%20da%20Sociedade%20Brasileira%20de%20Matem%C3%A1tica%20/%20Bulletin%20of%20the%20Brazilian%20Mathematical%20Society&rft.date=2010&rft.volume=40&rft.spage=587%20-%20612&rft.epage=587%20-%20612&rft.eissn=1678-7544&rft.issn=1678-7544&rft.au=GARIBALDI,%20Eduardo&LOPES,%20Artur&THIEULLEN,%20Philippe&rft.genre=article |
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